Question: Abe, Bobby, Charles, Devin and Edwin are the participants in a race. How many different 1st-2nd-3rd place outcomes are possible if there are no ties? Two different outcomes to include are Bobby-Devin-Edwin and Devin-Bobby-Edwin.
There are $5$ possibilities for the first place finisher.  After first place is determined, there are $4$ remaining possibilities for the second place finisher.  Finally, there are $3$ possibilities for third place once the first two are determined.  Thus there are $5\cdot4\cdot3=\boxed{60}$ 1st-2nd-3rd place outcomes.